Dissociation constants of acetic acid and primary ... - ACS Publications


Dissociation constants of acetic acid and primary...

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Anal. Chem. 1980, 5 2 , 1598-1601

1598

techniques (22) for chopping a laser beam a t megahertz frequencies and high frequency lock-in amplification both exist, suggesting the practicability of a more quantitative dispersive PAS of solids. T h e corresponding high frequency FTPAS experiment probably can be performed using the train of nanosecond duration white light pulses from a synchrotron as t h e intense high frequency light source. Such an exotic FTPAS experiment offers little prospect of an advantage over megahertz dispersive PAS a t visible wavelengths unless speed of acquisition of a broad band spectrum assumes paramount importance.

C. K. N. Patei, A . C.Tam, and R. J. Kerl, Appl. Phys. Lett., 34, 467 (1979). A. Hordvik and H. Schlossberg, Appl. O p t . , 11, 101 (1977). M. M. Farrow, R. K. Burnham, M. Auzanneau, S . L. Olsen, N. Purdie, and E. M. Eyring, Appl. O p t . , 17, 1093 (1978). H. K. Wickramasinghe, R. C. Bray, V. Jipson, C. F. Quater, and J. R. Salcedo, Appl. Phys. Lett., 33, 923 (1978). M. M. Farrow, R. K. Burnham, and E. M. Eyring, Appl. Phys. Lett., 33, 735 (1978). G. Busse and B. Builemer, Infrared Phys., 18, 255 (1978). M. G. Rockley, Chem. Phys. Left., 88, 455 (1979). P. R. Griffiths, "Chemical Infrared Fourier Transform Spectroscopy", John Wiley and Sons, New York, 1975, p 40. C. Foskett and T. Hirschfeld, Appl. Spectrosc., 31, 239 (1977). Representative examples are: W. N. Delgass, G. L. Hailer, R. Keilerrnan, and J. H. Lunsford, "Spectroscopy in Heterogeneous Catalysis", Academic Press, New York, 1979, Chapter 4. R. Tilgner and E. Lushcer, Z . Phys. Chem. N.F., 111, 19 (1978). M. J. Adams. B. C. Beadle, A. A. King, and G. F. Kirkbright, Ana/yst (London), 101, 553 (1976). J. J. Freeman, R. M. Friedman, and H. C. Reichard, J . Phys. Chem., 84, 315 (1980). J. Sapriel, "Acousto-Optics", John Wiley and Sons, New York, 1979, Chapter 7.

ACKNOWLEDGMENT We have had numerous interesting discussions with Joel M. Harris, University of Utah, and also thank William A. Koldewyn, IBM-Boulder, for suggestions regarding the He-Ne laser interferometric referencing system.

LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) (8)

RECEIVED for review December 26, 1979. Accepted June 20, 1980. T h e blood studies performed by LBL and WLC were made possible by Grant HL 23378-01 from the National Heart,

A. G. Bell, A m . J. Sci., 20, 305 (1880). A. G. Bell, Phil. Mag. 11, 510 (1881). A Rosencwaig, Opt. Commun., 7, 305 (1973). A. Rosencwaig, Anal. C h e m . , 47, 592 (1975). A. Rosencwaig and A. Gersho, J . Appl. Phys., 47, 64 (1976). A. Rosencwaig, Adv. Electron. Electron Phys., 48, 207 (1978) D. Cahen and H. Gam, Anal. Chem., 51, 1865 (1979). J. W.-P. Lin and L. P. Dudek, Anal. C h e m . , 51, 1627 (1979).

Lung, and Blood Institute. T h e applications of F T P A S to the study of solid samples were financed by a contract from the Department of Energy (Office of Basic Energy Sciences).

Dissociation Constants of Acetic Acid and Primary Phosphate Ion and Standards for pH in 10, 20, and 40 wt % EthanoVWater Solvents at 25, 0, -5, and -10 "C Roger G. Bates," H.

P. Bennetto,'

and Munessar Sankar2

Department of Chemistry, University of Florida. Gainesville, Florida 326 1 I

Earlier work leading to the standard potential of the Ag/AgCI electrode in 10, 20, and 40 wt YO ethanoVwater solvents at 25, 0, -5, and -10 O C has been extended to the study of an acetate buffer solution and a phosphate buffer solution in the same media at these four temperatures. Cells without liquid junction,

Pt;H2(g, 1 atm)IHA,A,NaClIAgCl;Ag were used to determine the dissociation constants of acetic acid and H P 0 4 - In these ethanol/water media. Buffer solutions composed of (a) acetic acid (0.05 m ) , sodium acetate (0.05 m ) and (b) KH2P04(0.025 m ) , Na2HP04(0.025 m ) , where m Is molality, are useful as standards for pH measurements.

I n a recent contribution ( I ) , we have reported a determination of the standard potential of the silver-silver chloride electrode in 10, 20, and 40 wt % ethanol/water solvents a t four temperatures: 25,0, -5, and -10 "C. The results lay the groundwork for thermodynamic studies, by emf methods, of both weak and strong electrolytes in these solvent media a t temperatures below 0 "C. We have now investigated the On leave from Queen Elizabeth College, University of London, 1979. On leave from the University of Durban-Westville, South Africa, 1977-78. 0003-2700/80/0352-1598$01 OO/O

dissociation of two weak acids of different charge types, namely, acetic acid and H,PO,-, and have determined conventional p H values for an acetate buffer solution and a phosphate buffer solution in ethanol/water media at subzero temperatures. These solutions are useful as reference standards for p H measurements and control in such processes as the separation of the protein fractions of blood plasma by the Cohn method (2).

EXPERIMENTAL Glacial acetic acid was purified by repeated fractional freezing under nitrogen. The melting point of the product rose in five stages of purification from 14.5 t o 16.602 "C; this final value is to be compared with the literature value of 16.606 "C. Sodium acetate and sodium chloride were crystallized twice from doubly distilled water. The former was dried at 120 "C overnight and finally for 3 h under vacuum at 95 "C. The NaCl was dried at 130-150 "C in air. The KHzP04 and Na2HP04 were NBS Standard Reference Materials 186Ic and 186IIc; they were dried for 2 h under vacuum at 100 "C. Stock solutions containing equal molal ratios, HAc/NaAc and KH2PO4/Na2HPO4,in the appropriate mixture of water and absolute ethanol were prepared. The cell solutions were prepared by weight from these stock solutions, the ethanol/water solvents, and NaCl. Limited solubility in 40 wt % ethanol precluded the measurements of phosphate-NaCl solutions in this solvent at 0 "C and below. Likewise, some problems were encountered with freezing of the acetate buffers in 10 w t 70ethanol at -10 "C. One of the phosphate buffer solutions in 10% ethanol also froze after some time at -10 "C, but no difficulty was experienced in obtaining c 1980 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 52, NO. 11, SEPTEMBER 1980

Table I. Electromotive Force of Cells A and B for Three EthanolIWater Solvents at 25, 0, -5, and -10 "C, in Volts mc1,

t, "C

mol

10% EtOH 20% EtOH

kg-'

40% EtOH

Cell A (0.05 m HAC + 0.05 m NaAc) 25

0.03 0.02 0.01 0.03 0.02 0.01 0.03 0.02 0.01 0.03 0.02

0 -5 -10

0.59547 0.60592 0.62375 0.57736 0.58690 0.60321 0.57358 0.58290 0.59891

(solutions froze)

0.01

0.59773 0.60818 0.62600 0.57802 0.58757 0.60394 0.57378 0.58320 0.59913 0.56948 0.57864 0.59429

Cell B (0.025 m KH,PO, 25

0.03 0.02 0.01 0.03 0.02 0.01 0.03 0.02 0.01 0.03 0.02 0.01

0 -5 -10

0.72977 0.74099 0.7 5954 0.7 067 6 0.71705 0.73409 0.70211 0.71224 0.72902 0.69751 0.7 07 47 0.72396

+ 0.025

0.73518 0.74653 0.76535 0.71160 0.72207 0.73938 0.70670 0.7 17 02 0.73403 0.701 69 0.71 1 8 4 0.72858

0.61138 0.62194 0.63983 0.5941 2 0.60372 0.62012 0.59052 0.60001 0.61606 0.58691 0.59626 0.61190

m Na,HPO,) 0.73934 0.75125 0.7707 5

(salts incompletely soluble)

RESULTS AND DISCUSSION T h e cells used for the measurements can be represented by Pt;H,(g, 1 atm)IHAc(0.05 m),NaAc(0.05 m ) , NaCUmcl) IAgC1;Ag (A) and P t ; H 2 ( g , 1 a t m ) I K H 2 P 0 4 ( 0 . 0 2 5m),Na2HPO4(0.025m ) , NaCl(mdIAgC1;Ag (B) where Ac is acetate and m is molality (moles per kilogram of mixed solvent). T h e observed data, corrected to a partial pressure of hydrogen of 1 a t m (101.325 kPa) as described earlier ( I ) , are listed in Table I. T h e relationship between the emf ( E ) ,the standard emf of the cell (EO),and the thermodynamic p K value for each of the acids was formulated as follows:

pK'

E

pK

-

PI =

( E - EO)F 2.3026RT

buffer ratio mac,d/mbase,that is, mHAc/mAc, was obtained by correcting t h e stoichiometric molalities (0.05) for t h e dissociation of acetic acid. In order to make this small correction, concentrations of hydrogen ion were derived from the paH obtained as described below. For the phosphate system, n = 2 ; hydrolysis of the phosphate ions was so slight t h a t macid/mbase did not depart significantly from unity. T h e conventional activity p H (-log aH) values for the chloride-free acetate and phosphate buffers were calculated from the limiting value, p(~~y,-l)O, of the acidity function P(aH?'Cl)

a t mcl = 0:

T h e convention (4)

was utilized, with A , t h e ion-size parameter, = 4.57 A; this is the same as i t s conventional value (1.5/B)in aqueous solutions ( 3 ) . This value, which was chosen earlier t o derive paH in methanol-water solvents ( 4 ) , was also used to calculate pK' by Equation 1. Hydrolysis of the acidic and basic species makes a negligible contribution to the ionic strength of these solutions. Hence, for acetate buffers

I = 0.05 + mcl

equilibrium values of the emf before freezing occurred. Nevertheless, it is unlikely that this buffer solution will prove useful for pH control at -10 "C. The preparation of electrodes and other experimental details were the same as in the earlier work ( I ) . Again the cells displayed excellent stability; final emf values at 25 "C, obtained after the measurements at 0, -5, and -10 "C were concluded, usually agreed with the initial values within 0.06 mV. In most instances, cells were measured in duplicate, the two measurements agreeing, on the average, to about 0.05 mV.

macid + + log mcl + log mbase

where I is the ionic strength, A and R are constants of t h e Debye-Huckel theory ( I ) , and n is a coefficient dependent on t h e charge type of the acid-base pair. The p K was determined by linear regression methods from the values of pK' for each solution studied. For the acetate system, n = 0. The

1599

(5)

and for the phosphate buffers

I = 0.1 + mcl

(6)

T h e standard potential Eo (molality scale) of the cell was reported in our earlier paper ( I ) . Apparent values (EO') were a function of t h e ionic strength and the choice of ion-size parameter A. The criterion of a minimum in the standard deviation for regression from the linear plot of E" as a function of I was adopted. This procedure yielded reasonable values of ii of 4.8 to 6.3 8, in 10% ethanol and 4.0 t o 5.2 b, in 40% ethanol. At the intermediate composition (20% ethanol), however, A appeared t o range from 6.2 to 8.5 b, a t t h e four temperatures, 25 to -10 "C, despite a high degree of precision in the measurements. This anomaly has prompted us to re-examine the calculation of Eo, and for this purpose we have now applied t h e activity coefficient equation of Bennett0 and Spitzer ( 5 ) ,based on a polarizable spheres model. The results of this treatment are in good agreement with the earlier calculations at 10 and 40% ethanol but yield lower values of A and F? for the 20% ethanol solvent. T h e mean difference of about 0.3 mV corresponds to 0.005 in pH. The values of i found by this procedure vary linearly with the temperature, but there is a suggestion t h a t 8 , a t a given temperature, passes through a minimum a t a solvent composition between 10 and 20 wt 70 ethanol. T h e results of this calculation are compared with the previous results in Table 11. T h e mean values of Eo, given in the last column, were used to derive pK' and p(aHyc1) by Equations 1 and 2, respectively. T h e values of p ( ~ H y ca~t ) ~ mcl = 0 were determined by linear regression of p(aHycl)as a function of mcl, whereas p K at I = 0 was found by linear regression of pK' vs. I . The results for p K and ~ C Z are H summarized in Table 111. These quantities are self-consistent, that is, they are interrelated through the identity

derived from the mass law. As indicated above, n = 0 for

1600

ANALYTICAL CHEMISTRY, VOL. 52, NO. 11, SEPTEMBER 1980

54-

Acetate B u f f e r

52-104

Pa H

50

48-

I /

0

/

0

IO

20

wt

30

10

40

% ElOH

~~

~~

~~

as a function of the composition of the ethanollwater solvent acetic acid and n = 2 for H,PO,-. The changes of pa^ for the two buffer solutions with temperature and solvent composition are shown in Figures 1 and 2. Spivey and Shedlovsky (9) have determined the dissociation constant of acetic acid in ethanol/water mixtures by means of measurements of electrolytic conductance over a range of solvent compositions a t 0, 25, and 35 "C. Our results in 10, 20, and 40 wt % ethanol can be compared with theirs a t 25 and 0 "C. For this purpose, we have corrected their values on the molar concentration scale (pK,) to values on the molality scale (pK,) by use of the solvent density, do:

~

Table 11. Standard Emf (E" ) o f the Cell at Four Temperatures Previous results

Recalculated results

( 11

t,

;,A

:,

E",V

mean

E",V

E",V

0.21455 0.22614 0.22763 0.22878

0.21457 0.22617 0.22768 0.22881

0.20750 0.21750 0.21849 0.21910

0.20761 0.21766 0.21866 0.21926

0.19446 0.20970 0.21183 0.21385

0.19448 0.20971 0.21190 0.21390

A

10%ethanol 25 0 -5 -10

4.8 5.8 6.2 6.3

0.21458 0.22619 0.22773 0.22886

5.6 6.15 6.2 6.35

+

pK, = pK, log do (8) The agreement between the two determinations is excellent in 10 and 40 wt % ethanol; the differences amount to 0.004 and 0.007 a t 25 and 0 "C, respectively, in 10% ethanol and to 0.003 and 0.006, respectively, in 40% ethanol. A larger discrepancy (0.017 unit) appears in 20% ethanol at 25 "C, and a still larger difference of 0.050 unit is found at 0 "C. A plot of pK, as a function of wt 70ethanol (Figure 3) makes it clear that this latter result is inconsistent both with their other data and with ours and may be presumed to be in error. As far as we are aware, there have been no previous attempts to provide reference solutions for the standardization

20% ethanol 25

0 -5 -10

6.2 8.0 8.5 8.2

0.20771 0.21781 0.21883 0.21941

5.5 6.1 6.2 6.25

40% ethanol 25 0 -5 -10

4.0 4.5 4.8 5.2

0.19450 0.20972 0.21197 0.21395

4.8 5.2 5.25 5.3

30

Yo EtOH

Figure 2. pa, of the phosphate buffer solution at four temperatures

as

a function of the composition of the ethanol/water solvent ~

20 wt

Figure 1. pa, of the acetate buffer solution at four temperatures

"c

Phosphate Buffer

Table 111. pK o f Acetic Acid and H,PO,- in Four EthanolIWater Solvents. Conventional paH Values for an Acetate and a Phosphate Buffer H,O t, " C

PKa

1 0 % EtOH

WH

PK

20% EtOH

PaH

PK

40% EtOH

PaH

PK

PaH

4.967 5.021 5.044 5.075

5.539 5.580 5.605 5.628

5.39 5 5.445 5.470 5.498

7.310 7.508 7.569 7.638

8.287

7.597

0.05 m HAC + 0.05 m NaAc 25 0 -5

4.756 4.770

4.67 0 4.687

-1b

4.919 4.956 4.974

4.822 4.861 4.881

0.025 rn KH,PO, 25 0 -5 -10

7.198 7.313

6.865 6.984

7.529 7.695 7.758 7.825

+

5.075 5.131 5.149 5.177

0.025 m Na,HPO,

7.104 7.263 7.315 7.376

7.800 8.017 8.083 8.157

In H,O: pK of acetic acid from Ref. 6 and 7; pK of H,PO,- from Ref. 8.

Anal. Chem. 1980 52, 1601-1606

1601

identified with pH(S) in the operational definition of pH. Nevertheless, too little is yet known concerning the residual liquid-junction potential in these solvents at low temperatures to permit one to assess the internal consistency of the pH scale defined by these reference points. Measurements of pH under these extreme conditions are rendered difficult by the extraordinarily high resistance of the usual glass electrodes. In addition, modified reference electrodes will doubtless prove a necessity.

LITERATURE CITED (1) M. Sankar, J. B. Macaskill, and R. G. Bates, J . Solution Chem., 8, 887 (1979) (2) E. J Cohn, F. R. N. Gurd, D. M. Surgenor, B. A . Barnes, R . K. Brown, G. Deronaux. J. M. Gillesoie. F. W . Kahnt. W. F. Lever. C. H. Liu. D. Mittelman, R.'F. Mouton,~K:Schmid, and E. Urorna, J . Am: Chem. Sbc.. 72, 465 (1950). (3) R. G. Bates and E. A. Guggenheim. Pure Appl. Chem., 1, 163 (1960). (4) M. Paabo, R. A. Robinson, and R. G. Bates, J . Am. Chem. SOC.,87. 415 (1965). Faraday Trans. 7, 73, (5) H. P. Bennett0 and J. J. Spitzer, J . Chem. SOC., 1066 (1977). (6) H. S. Harned and R. W. Ehiers, J . Am. Chem. SOC.,54, 1350 (1932); 55, 652 (1933). (7) D. A. MacInnes and T. Shedlovsky, J . Am. Chem. SOC., 5 4 , 1429 (1932). (8) R. G. Bates and S.F. Fxree, J . Res. NaN. Bur. Stand., 34, 373 (1945). (9) H. 0. Spivey and T. Shedlovsky, J . Phys. Chern., 71, 2171 (1967). \

0

Spivey and Shedlovsky

0

Present work

- I

47T 0

20

10

wt

30

X EIOH

Figure 3. pK(molality scale) for acetic acid in ethanol/water mixtures a t 0 and 25 OC as a function of the composition of the solvent. Data in water are from Ref. 6 a n d 7

of p H measurements in ethanol/water media at temperatures below 0 "C. The values of PQHfor the acetate and phosphate buffers given in Table I11 may fill this need. When used as reference solutions, the PQH of these buffer solutions is

RECEIVED for review March 3, 1980. Accepted May 12, 1980. This work was supported in part by the National Science Foundation under Grant CHE76 24556. M.S. thanks the following organizations in the Republic of South Africa for financial assistance: t h e C.S.I.R., Ernest Oppenheimer Memorial Trust, and Sentrachem Ltd.

Determination of Oxidation States of Uranium in Uranium Dioxide Pellets by Two-step Flow-Coulometry Sorin Kihara,' Zenko Yoshida, Hiroshi Muto, Hisao Aoyagi, Yuji Baba, and Hiroshi Hashitani Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, Japan

A chemical method for analysis of distribution of oxidation states of metals in solids has been developed as a reference to other methods based on physical measurements. A solid is dissolved with a continuous flow of strong phosphoric acid from surface to bulk, and oxidation states of the dissolved ions are determined consecutively by two-step flow-coulometry. Strong phosphoric acid dissolves such solids as uranium or iron oxides to Ions whose oxidation states are the same as those in solids. The oxidized surface of about 20 A on a UOz pellet which had stood for about 10 years at room temperature in alr was estimated to be U02.05,and the O/U ratio decreased toward the bulk until 0.1 pm. After the pellet was heated for 10 h at 300 or 430 O C in air, the oxidized surface layer increased to about 8 pm (400 8, of powdered U308 UO,+,, 0.66 > x > 0.01) or about 820 pm (370 prn of powdered U308 -t 3 prn of U,08 450 pm of UOZ+,, 0.66 > x > 0.01), respectively.

+

+

Analysis of oxidation states of metals in solids based on physical measurements gives abundant information on ma0003-2700/80/0352-1601$01 .OO/O

terial science. These physical methods can be classified broadly into methods (1) for analysis of very thin layers a t the surface such as by X-ray photoemission spectrometry (XPS) or Auger electron spectrometry (AES) and methods ( 2 ) which give overall information on a solid such as measurements of conductivity or electromotive force (EMF). There are many difficulties still remaining with these methods. In the former, for example, pretreatment of the surface and composition of the matrix greatly affect the result of analysis, and, in the latter, interaction between sample and electrode and the presence of impurities often give serious trouble. Therefore, calibration by reference materials and careful evaluation of data obtained are required. Obviously, data obtained by chemical analyses offer many suggestions for the interpretation of results obtained by physical methods. Although analyses of oxidation states by chemical methods give rather quantitative results, most of the work using these methods has been done to obtain the overall oxidation state of a sample. Few attempts have been made to analyze oxidized films of solid surfaces or to determine distribution of oxidation states in a solid. The objective of our research was to develop a new independent method ;o investigate the distribution of oxidation 1980 American Chemical Society